论文标题
galerkin有限元方法用于可变底部形象上两个经典 - 布斯萨斯类型系统的数值解决方案
Galerkin finite element methods for the numerical solution of two classical-Boussinesq type systems over variable bottom topography
论文作者
论文摘要
我们考虑了两个“经典” Boussinesq类型系统在有限的底部地形的有限通道中建模长表面波的双向传播。这两个系统均来自1-D Serre-Green-Naghdi（SGN）系统。其中一个对于更强的底部变化有效，并且与Peregrine的系统相吻合，而另一个则有效对于较小的底部变化有效。我们使用标准的Galerkin-FINITE元素方法对两个系统的空间变量简单可变性初始值问题（IBVP）进行离散化，并证明$ l^2 $错误估计随之而来的半差异近似值。我们将这些方案与第四阶 - 明确的，经典的，经典的runge-kutta时间稳定过程相结合，并在可变底部的分散波传播的数值模拟中使用所得的完全离散的方法，具有多种边界条件，包括吸收较差的边界条件。我们详细描述了在每个系统下在各种可变底部环境下演变时孤立波发生的变化。我们通过将它们的模拟结果与SGN系统的模拟以及文献中的可用实验数据进行比较，评估了两个系统在近似这些流中的疗效。
We consider two `Classical' Boussinesq type systems modelling two-way propagation of long surface waves in a finite channel with variable bottom topography. Both systems are derived from the 1-d Serre-Green-Naghdi (SGN) system; one of them is valid for stronger bottom variations, and coincides with Peregrine's system, and the other is valid for smaller bottom variations. We discretize in the spatial variable simple initial-boundary-value problems (ibvp's) for both systems using standard Galerkin-finite element methods and prove $L^2$ error estimates for the ensuing semidiscrete approximations. We couple the schemes with the 4th order-accurate, explicit, classical Runge-Kutta time-stepping procedure and use the resulting fully discrete methods in numerical simulations of dispersive wave propagation over variable bottoms with several kinds of boundary conditions, including absorbing ones. We describe in detail the changes that solitary waves undergo when evolving under each system over a variety of variable-bottom environments. We assess the efficacy of both systems in approximating these flows by comparing the results of their simulations with each other, with simulations of the SGN-system, and with available experimental data from the literature.
